A local area network (“LAN”) may be wired or wireless. A wireless local area network (“wireless LAN” or “WLAN”) is a flexible data communications system implemented as an extension to, or as an alternative for, a wired local area network (“wired LAN”) within a building or campus. Using electromagnetic waves, WLANs transmit and receive data over the air, minimizing the need for wired connections. Thus, WLANs combine data connectivity with user mobility, and, through simplified configuration, enable movable LANs. Some industries that have benefited from the productivity gains of using portable terminals (e.g., notebook computers) to transmit and receive real-time information are the digital home networking, health-care, retail, manufacturing, and warehousing industries.
Manufacturers of WLANs have a range of transmission technologies to choose from when designing a WLAN. Some exemplary technologies are multicarrier systems, spread spectrum systems, narrowband systems, and infrared systems. Although each system has its own benefits and detriments, one particular type of multicarrier transmission system, orthogonal frequency division multiplexing (“OFDM”), has proven to be exceptionally useful for WLAN communications.
OFDM is a robust technique for efficiently transmitting data over a channel. The technique uses a plurality of subcarrier frequencies (“subcarriers”) within a channel bandwidth to transmit data. These subcarriers are arranged for optimal bandwidth efficiency as compared to conventional frequency division multiplexing (“FDM”), which can waste portions of the channel bandwidth in order to separate and isolate the subcarrier frequency spectra and thereby avoid inter-carrier interference (“ICI”). By contrast, although the frequency spectra of OFDM subcarriers overlap significantly within the OFDM channel bandwidth, OFDM nonetheless allows resolution and recovery of the information that has been modulated onto each subcarrier. In addition to the more efficient spectrum usage, OFDM provides several other advantages, including a tolerance to multi-path delay spread and frequency selective fading, good interference properties, and relatively simplified frequency-domain processing of the received signals.
For processing, an OFDM receiver typically converts a received signal from the time-domain into frequency-domain representations of the signal. Generally, conventional OFDM receivers accomplish this by sampling the timedomain signal and then applying Fast Fourier Transforms (“FFTs”) to blocks of the samples. The resulting frequency-domain data generally includes a complex value (e.g., magnitude component and phase component, or real component and imaginary component) for each respective subcarrier. The receiver typically applies an equalizer to the frequency-domain data before recovering the baseband data that was modulated onto each subcarrier. Primarily, the equalizer corrects for multi-path distortion effects of the channel through which the OFDM signal was transmitted. Some receivers may also use the equalizer to correct for other problems encountered with OFDM communications, such as, for example, carrier frequency offset (i.e., a difference between the transmitter and receiver frequencies), and/or sampling frequency offset (i.e., a difference between the transmitter and receiver sampling clock frequencies). Carrier frequency offset and sampling frequency offset can result in a loss of orthogonality between the subcarriers, which results in inter-carrier interference (“ICI”) and a severe increase in the bit error rate (“BER”) of the data recovered by the receiver. In any event, the equalizer of the OFDM receiver typically has one or more taps which receive a tap setting corresponding to the complex correction (e.g., real correction and imaginary correction, or magnitude correction and phase correction) for each subcarrier.
Historically, the equalizer taps have been initialized with (X/Y), which represents a division of a predetermined, stored frequency-domain representation of an expected OFDM signal (i.e., a “training symbol” or “X”) by the frequency-domain representation of the corresponding actual received signal (“Y”). Such initialization schemes are based on a simplified frequency-domain channel model that assumes orthogonality among the subcarriers, in which Y=C*X, where an actual received signal (Y) is merely a transmitted predetermined signal (X) times the channel response (C). In such a case, C=Y/X and thus, to compensate for the channel response, the equalizer is initialized with the inverse of the channel response (i.e., 1/C, or X/Y).
However, in digital data processing systems division operations are generally slower and require more memory than multiplication operations. Accordingly, some OFDM receivers implement the necessary division by divider circuits in hardware. But hardware divider circuits are undesirably expensive. Alternatively, other receivers approximate the division by resort to a lookup table. There, multiplication operations can be employed when the received training symbol (Y) is the input to the table and the output of the table is the inverse of the received training symbol (1/Y). The inverse (1/Y) is then multiplied by the actual training symbol (X) to form the tap initialization (X/Y), thus avoiding division operations. However, in order to get good results, the lookup tables must have undesirably large numbers of storage locations, which is also undesirably expensive. The present invention is directed to the correction of this problem.